House Speaker John Boehner, R-Ohio, has met privately with President Obama about the 'fiscal cliff.' / J. Scott Applewhite, AP

by Susan Davis, USA TODAY

by Susan Davis, USA TODAY

WASHINGTON -- President Obama and House Speaker John Boehner, R-Ohio, have exchanged new proposals to avert the year-end "fiscal cliff," but agreement on a final deal that can pass Congress remains elusive with less than three weeks remaining to reach an accord.

In an interview with ABC News, Obama said he believes Republicans will give on their opposition to raising tax rates. "I'm pretty confident that Republicans would not hold middle-class taxes hostage to trying to protect tax cuts for high-income individuals," he said. All of the George W. Bush era tax cuts expire Dec. 31. Democrats want to extend the current rates for all but the top 2%.

Meanwhile, Boehner called out the president from the House floor for stalling negotiations because Obama has not proposed enough spending cuts to appease Republicans. "The longer the White House slow-walks this process, the closer our economy gets to the fiscal cliff," Boehner warned.

Despite the public posturing, private talks between Obama and Boehner restarted following a Sunday meeting at the White House that Boehner described as "cordial." The White House sent a revamped proposal to Boehner on Monday. Michael Steel, a spokesman for Boehner, said the speaker responded with a counterproposal on Tuesday.

The Associated Press reported that the president offered to reduce his initial request for $1.6 trillion in new revenue to $1.4 trillion, but that Obama hasn't budged on raising the top rates. Boehner's spokesman said Republicans are still seeking further concessions on spending cuts. Republicans are "still waiting for the White House to identify what spending cuts the president is willing to make," Steel said. Obama and Boehner also spoke on the phone Tuesday evening, said a White House aide, who spoke on condition of anonymity because officials are not authorized to speak publicly.

Obama and Congress are trying to avoid harm to the U.S. economy when Bush-era tax cuts expire at the end of the year and billions of dollars in spending cuts to defense and domestic programs start to kick in shortly after. If taxes go up and the automatic spending cuts go into effect, the economy could be thrown into a recession by the third quarter of 2013.

Despite the looming deadline and ongoing policy divides, Obama and Boehner expressed optimism Tuesday that they could reach a deal. Senate Majority Leader Harry Reid, D-Nev., said Tuesday that negotiations would likely go down to the wire and dispelled hope that Congress would adjourn before the holidays. "I think it's going to be extremely difficult to get it done before Christmas, but it could be done," he said.

In recent days, Republicans have focused on three concessions that could inch Washington closer to a deal: raising the Medicare eligibility age, making wealthier seniors pay more for their benefits, and changing the way cost-of-living adjustments are calculated for Social Security benefits. Democrats traditionally oppose all three of those proposals.

Obama has not ruled out raising the Medicare eligibility age. "When you look at the evidence, it's not clear that it actually saves a lot of money," he told ABC News. "But what I've said is let's look at every avenue, because what is true is we need to strengthen Social Security, we need to strengthen Medicare for future generations, the current path is not sustainable because we've got an aging population and health care costs are shooting up so quickly."

Minority Leader Nancy Pelosi, D-Calif., said Democrats would agree to changes on entitlements as long as the middle class would not be hurt. "It's not about the price of the high-end tax cut. It's about the money it generates," she said. "But it is not to burden the middle income in order to have bigger tax cuts at the high end."